When he's had tightness in his elbow in the past, he's been able to loosen it up.
"I'd say it's a weather issue," Garza said. "I'm just not used to pitching in the cold weather a lot. The best thing to do now is listen to them and do what's right.
"It hasn't gotten worse. It just hasn't gotten better."
Who will start on Sunday will depend on who is used out of the bullpen in Saturday's game. Cubs manager Mike Quade said it may be similar to a Spring Training game in which everyone chips in. The Cubs have Monday off.
"He's got a little stiffness in his elbow, and we're going to be real careful with this guy, skip him and give him some rest," Quade said of Garza (2-4, 3.72 ERA).
Garza is scheduled to see team orthopedic specialist Dr. Stephen Gryzlo on Monday.
"He had a great side [session] two days ago," Quade said. "They cut it short because they loved it. He felt a little tenderness yesterday, a little tightness today, so we're not taking a chance."
Quade said the situation is "literally day to day."
One option considered briefly was Randy Wells, who is scheduled to make his second rehab start on Sunday for Triple-A Iowa. He's coming back from a strained right forearm, which he felt after his first start on April 4.
James Russell, who has started four games in Andrew Cashner's spot as the righty rehabs from a strained right rotator cuff, will most likely start. Russel is 0-4 with a 10.05 ERA in his four starts and 1-4 with a 6.26 ERA overall. The left-hander threw 39 pitches over three innings in relief on Friday in the series opener.
"The options tomorrow are everybody," Quade said. "It literally could be a Spring Training type of game, where a couple here, a couple there."
Garza was looking forward to facing the Red Sox. He is 7-4 with a 3.83 ERA in 19 games against Boston and 5-3 with a 3.81 ERA in nine starts at Fenway Park.
"I haven't missed a start for anything," Garza said. "This is a first. It stinks. I feel like I let my team down. I have to look at the big picture. What if it gets worse? What if I damage something?"
"The only thing I said," Quade said, "was, 'Have you had any trouble with this in the past?' and he said, 'Nothing to concern myself with,' and I said, OK, fine.'"
Garza will be the third Cubs starter to miss a start this season. Cashner and Wells went on the disabled list after their first starts in the first five days of the season.